Answer: -13.05 m/s²
Explanation:
To find the acceleration of the arrow, we can use this kinematic formula:
d = v₀t + (1/2)at², where:
- d is the displacement
- v₀ is the initial velocity (or speed in this case)
- a is the acceleration
- t is the time
We are given:
- d = 45 m
- v₀ = 36.3 m/s
- t = 3.7
Let's substitute these values into the formula:
45 = 36.3(3.7) + (1/2)a(3.7)²
Solve for a:
-89.31 = (1/2)a(3.7)²
-178.62 = a(3.7)²
a = -13.047
The acceleration of the arrow being shot upwards is approximately -13.05 m/s².
The negative sign indicates that the acceleration is directed downwards, which is consistent with the deceleration experienced by the arrow as it reaches the peak of its trajectory.
